Figure 1: Triangle flows for weighted clustering coefficient
Source: Tabak et al.,2014.
Figure 2: Hypothetical directional weighted network composed of six nodes and eight directional links across the nodes
Figure 3: Average connectivity measures: In this table, we present the cross-sectional averages for network density, weighted clustering coefficient and reciprocity measures for all months between January 2006 - November 2015. We construct our network measures using intraday quotes and trades for all stocks traded in Borsa Istanbul.
Figure 4: Cumulative Returns For Univariate Global Connectivity (Network Density) Portfolios: In this figure we present the cumulative return for equally weighted and value weighted portfolios that mimics an investor who has a long position in stocks with low network density and a short position with equal size in stocks with high network density along with the cumulative returns for the market index (BIST 100). All returns are denominated in U.S. Dollars.
Figure 5: Cumulative Returns For Univariate Local Connectivity (WCC) Portfolios: In this figure we present the cumulative return for equally weighted and value weighted portfolios that mimics an investor who has a long position in stocks with low average local connectivity (weighted clustering coefficient) and a short position with equal size in stocks with high average local connectivity along with the cumulative returns for the market index (BIST 100). All returns are denominated in U.S. Dollars.
Figure 6: Cumulative Returns For Univariate Network Reciprocity Portfolios: In this figure we present the cumulative returns for equally weighted and value weighted portfolios that mimics an investor who has a long position in stocks with low network reciprocity and a short position with equal size in stocks with high network reciprocity along with the cumulative returns for the market index (BIST 100). All returns are denominated in U.S. Dollars.
Figure 7: Difference in Univariate Portfolio Returns: In this figure, we present the difference in equally weighted and value weighted zero cost network density (ND) and weighted clustering coefficient portfolios (WCC). The portfolios mimic an investor who has a long position in stocks with low ND (WCC) and a short position with equal size in stocks with high ND (WCC). The difference is obtain via subtraticting the cumulative return of zero cost portfolio constructed with ND from the zero cost portfolio constructed with WCC in a given month. We test whether the means of cumulative return series are different or not via Welch two-sample t-test. We fail to reject the null hypothesis that the means cumulative returns are the same with corresponding p-values 0.6843 and 0.9384 for equally weighted and value weighted portfolios.
Table 1: Descriptive Statistics: In this table, we present the descriptive statistics for firm-specific factors that are calculated for all stocks that are traded in BIST between January 2006 - April 2017. RETURN represents the monthly log returns. BETA is the systematic risk factor. SIZE is the logarithm of the end of month market capitalization. BTM is the book-to-market ratio. MOM is the momentum variable. ILLIQ is the illiquidity measure. †indicates x104. MAX is the maximum daily return within a month. IVOL is the idiosyncratic volatility. REVis the return reversal measured by one-month lag return. ND is the network density which is also our global connectivity measure. WCC is the average weighted clustering coefficient, our average local connectivity measure. RCP denotes the network reciprocity. In Panel A, we respectively present number of observations, mean, standard deviation, minimum and maximum values for each variables in our sample. In Panel B, we present the pairwise correlations. * indicates statistical significance at 1% level
Variable
Panel A: Descriptive Statistics Panel B: Pairwise correlations
Obs Mean Std. Dev. Min Max RETURN SIZE BETA BTM MOM ILLIQ† IVOL MAX REV ND WCC RCP
RETURN 37760 -0.01 0.16 -1.83 1.82 1
SIZE 37760 4.59 1.96 -0.48 10.10 -0.01* 1
BETA 37758 0.73 0.40 -6.72 5.01 -0.14* 0.17* 1
BTM 37760 -0.24 0.88 -6.16 3.61 0.08* -0.28* 0.02* 1
MOM 37203 0.06 0.50 -0.94 20.04 -0.03* 0.09* -0.00 -0.1401* 1
ILLIQ† 37756 0.02 0.47 0.00 43.98 -0.00 -0.06* -0.04* 0.0067 -0.01 1
IVOL 37758 0.02 0.01 0.00 0.17 0.13* -0.24* 0.0341* -0.01* 0.11* 0.04* 1
MAX 37760 0.06 0.04 0.00 0.90 0.22* -0.14* 0.2065* 0.01 0.04* 0.01 0.81* 1
REV 37328 -0.01 0.16 -1.83 1.82 -0.02* 0.07* 0.0235* -0.09* 0.33* 0.00 0.01 -0.01 1
ND 37760 0.19 0.11 0.00 0.70 0.11* 0.52* 0.3003* -0.06* 0.12* -0.06* 0.13* 0.20* 0.0392* 1
WCC 37760 0.56 0.16 0.00 0.97 0.12* 0.52* 0.2990* -0.07* 0.14* -0.11* 0.12* 0.19* 0.04* 0.93* 1
RCP 37760 0.69 0.11 0.00 0.94 0.09* 0.21* 0.2367* -0.09* 0.09* -0.13* 0.20* 0.25* 0.02* 0.76* 0.80* 1
Table 2: Average portfolio characteristics: This table presents average characteristics for quintile portfolios based on network connectivity measures.
Specifically, Panel A, B and C respectively present the portfolios formed based on monthly network density, weighted clustering coefficient and network reciprocity measures. Low represents the portfolio consisting stocks with the lowest connectivity measures. Similarly, High represents the portfolio consisting stocks with the highest connectivity measures. The table reports the time-series averages of monthly average connectivity and various firm-specific measures for each quintile. High-Low represents the zero investment network connectivity portfolio which mimics the returns of an investor who has a long position in high connectivity portfolio and a short position of equal size in the low connectivity portfolio. t-statistics for each value is presented in parenthesis where they are corrected by the Newey-West procedure. BETAis the systematic risk factor.SIZEis the logarithm of the end of month market capitalization.
BTMis the book-to-market ratio. MOMis the momentum variable. ILLIQis the illiquidity measure. ‡indicatesx105. MAXis the maximum daily return within a month. IVOLis the idiosyncratic volatility. REVis the return reversal measured by one-month lag return. NDis the network density which is also our global connectivity measure.WCCis the average weighted clustering coefficient, our average local connectivity measure. RCPdenotes the network reciprocity.
Panel A: ND quintile portfolios
Low 2 3 4 High High-Low
ND 0.069 0.124 0.170 0.230 0.360 0.290
(30.07) (48.39) (64.45) (85.39) (122.83) (99.84)
SIZE 3.587 4.010 4.272 4.828 6.257 2.670
(71.85) (113.45) (132.75) (181.79) (157.67) (35.01)
BTM 0.163 0.182 0.242 0.286 0.313 0.150
(7.34) (8.47) (11.49) (14.34) (12.56) (7.64)
BETA 0.589 0.680 0.734 0.783 0.905 0.315
(41.69) (47.68) (46.72) (50.47) (72.36) (32.62)
ILLIQ‡ 6.777 0.024 0.013 0.005 0.001 -6.775
(4.70) (9.25) (8.04) (9.68) (9.83) (-4.70)
MOM 0.042 0.050 0.055 0.086 0.137 0.095
(1.69) (1.84) (1.91) (2.74) (4.08) (7.46)
IVOL 0.019 0.019 0.022 0.024 0.025 0.006
(54.89) (48.50) (53.28) (61.48) (68.44) (15.79)
MAX 0.052 0.056 0.064 0.072 0.077 0.025
(36.66) (33.97) (38.02) (41.83) (43.28) (25.75)
Panel B: WCC quintile portfolios
Low 2 3 4 High High-Low
WCC 0.346 0.484 0.562 0.641 0.764 0.419
(51.76) (105.35) (150.42) (193.97) (285.93) (75.52)
SIZE 3.568 3.937 4.194 4.749 6.502 2.934
(75.88) (118.54) (142.54) (181.79) (194.53) (46.18)
BTM 0.132 0.184 0.261 0.303 0.307 0.174
(6.09) (8.30) (12.41) (14.70) (12.06) (10.05)
BETA 0.597 0.682 0.728 0.774 0.909 0.312
(41.89) (46.14) (47.59) (47.40) (80.06) (33.28)
ILLIQ‡ 6.780 0.026 0.012 0.005 0.001 -6.780
(4.70) (8.58) (8.83) (10.30) (9.97) (-4.70)
MOM 0.031 0.038 0.069 0.098 0.134 0.103
(1.24) (1.42) (2.37) (3.13) (3.98) (8.17)
IVOL 0.019 0.019 0.022 0.025 0.024 0.004
(54.47) (47.58) (52.18) (61.85) (65.85) (12.63)
MAX 0.052 0.056 0.066 0.075 0.073 0.021
(36.68) (33.27) (38.38) (43.48) (40.73) (22.14)
Panel C: RCP quintile portfolios
Low 2 3 4 High High-Low
RCP 0.539 0.651 0.702 0.749 0.814 0.275
(103.28) (192.08) (222.59) (250.39) (315.95) (53.54)
SIZE 4.257 4.384 4.490 4.619 5.202 0.944
(67.41) (113.36) (127.94) (153.43) (109.87) (9.60)
BTM 0.163 0.128 0.196 0.292 0.406 0.243
(7.00) (6.23) (8.93) (13.27) (17.71) (11.84)
BETA 0.603 0.697 0.745 0.787 0.859 0.255
(47.14) (49.75) (52.18) (50.20) (52.59) (20.52)
ILLIQ‡ 6.720 0.051 0.017 0.033 0.005 -6.710
(4.68) (4.12) (8.88) (1.40) (4.84) (-4.68)
MOM 0.054 0.039 0.051 0.073 0.153 0.099
(2.13) (1.46) (1.79) (2.31) (4.55) (7.76)
IVOL 0.019 0.018 0.020 0.023 0.030 0.011
(56.30) (46.12) (51.44) (60.47) (72.67) (29.40)
Table 3: Univariate Portfolio Analysis - Quintile portfolios based on global connectivity (network density): In this table, we present the equally and value-weighted returns of quintile portfolios. At the end of each month, we sort our stocks into quintile portfolios based on global connectivity (network density) measures. We follow the portfolio returns for the next one, three and six months. Panel A,B and C present the findings for one, three and six months holding period, respectively. The four-factor↵is obtained through regressing the portfolio returns on the market return (BIST100), and size (SMB) and profitability (HML) ofFama and French(1993) and the momentum factor (UMD) ofCarhart(1997). High-Low represents the zero investment network density portfolio which mimics the returns of an investor who has a long position in high density portfolio and a short position of equal size in the low density portfolio. Last two rows of each panel present the t-statistic and p-values of the corresponding average return and ˆ↵estimates for the zero-investment (High-Low) portfolio where t-stats are corrected by the Newey-West procedure.
Panel A: Holding Period = 1 month
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.003 0.010 0.002 0.010
Panel B: Holding Period = 3 months
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low -0.001 0.006 -0.003 0.005
Panel C: Holding Period = 6 months
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.000 0.004 -0.001 0.005
Table 4: Univariate Portfolio Analysis - Quintile portfolios based on average local connectivity (WCC): In this table, we present the equally and value-weighted returns of quintile portfolios. At the end of each month, we sort our stocks into quintile portfolios based on average connectivity measures (WCC). We follow the portfolio returns for the next one, three and six months. Panel A,B and C present the findings for one, three and six months holding period, respectively. The four-factor↵is obtained through regressing the portfolio returns on the market return (BIST100), and size (SMB) and profitability (HML) of Fama and French(1993) and the momentum factor (UMD) ofCarhart(1997). High-Low represents the zero investment network density portfolio which mimics the returns of an investor who has a long position in high density portfolio and a short position of equal size in the low density portfolio. Last two rows of each panel present the t-statistic and p-values of the corresponding average return and ˆ↵estimates for the zero-investment (High-Low) portfolio where t-stats are corrected by the Newey-West procedure.
Panel A: Holding Period = 1 month
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.004 0.011 0.003 0.011
Panel B: Holding Period = 3 months
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.000 0.007 -0.001 0.006
Panel C: Holding Period = 6 months
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.000 0.003 -0.001 0.005
Table 5: Univariate Portfolio Analysis - Quintile portfolios based on network reciprocity: In this table, we present the equally and value-weighted returns of quintile portfolios. At the end of each month, we sort our stocks into quintile portfolios based on network reciprocity measures (RCP). We follow the portfolio returns for the next one, three and six months. Panel A,B and C present the findings for one, three and six months holding period, respectively. The four-factor ↵is obtained through regressing the portfolio returns on the market return (BIST100), and size (SMB) and profitability (HML) of Fama and French(1993) and the momentum factor (UMD) ofCarhart(1997). High-Low represents the zero investment network density portfolio which mimics the returns of an investor who has a long position in high reciprocity portfolio and a short position of equal size in the low reciprocity portfolio. Last two rows of each panel present the t-statistic and p-values of the corresponding average return and ˆ↵estimates for the zero-investment (High-Low) portfolio where t-stats are corrected by the Newey-West procedure.
Panel A: Holding Period = 1 month
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.001 0.008 0.000 0.007
Panel B: Holding Period = 3 months
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.000 0.006 -0.001 0.006
Panel C: Holding Period = 6 months
Equally-Weighted Portfolios Value-Weighted Portfolios Average Return Four Factor ↵ Average Return Four Factor ↵
Low 0.000 0.004 -0.001 0.004
Table 6: Multivariate Portfolio Analysis : 5x5 portfolios on global connectivity (network density) and firm-size
This table presents the characteristics of multivariate portfolios. At the beginning of each month, we divide the sample into size quintiles based on log market capitalization of previous quarter.
Then, we divide each quintile into five groups based on previous month’s network density measures which proxy for global connectivity. Panel A represents the time-series average of average monthly returns in each portfolio. High-Low is the average difference between High and Low connectivity portfolios. t-stat and p-value corresponds to the t-statistics and p-value of the zero-cost difference portfolio where t-stats are corrected by the Newey-West procedure. Panel B corresponds to the time-series average of the average market capitalization of each portfolio. Panel C corresponds to the time-series averages of the average network density in each portfolio.
Panel A: Average Portfolio Return
Small Firm 2 3 4 Big
Low ND 0.008 -0.001 0.006 0.003 -0.001
2 0.000 0.003 -0.005 0.000 -0.003
3 -0.016 -0.007 -0.014 -0.007 -0.004 4 -0.020 -0.014 -0.007 -0.009 -0.003 High ND -0.027 -0.013 -0.012 -0.003 -0.004 High-Low -0.035 -0.012 -0.018 -0.005 -0.002 t-stat (-4.84) (-1.81) (-3.45) (-1.05) (-0.42) p-value 0.00 0.04 0.00 0.15 0.34
Panel B: Average Size
Small 2 3 4 Big
Low ND 1.207 2.418 3.446 4.603 6.268
2 2.016 3.063 3.835 4.777 6.377
3 2.380 3.322 4.109 5.012 6.540
4 2.833 3.866 4.704 5.619 7.146
High ND 3.889 5.217 6.085 7.168 8.932
Panel C: Average Network Density (ND)
Small 2 3 4 Big
Low ND 0.059 0.070 0.073 0.073 0.071
2 0.123 0.124 0.125 0.125 0.124
3 0.169 0.170 0.170 0.171 0.171
4 0.225 0.228 0.230 0.233 0.234
High ND 0.320 0.336 0.353 0.363 0.425
Table 7: Multivariate Portfolio Analysis : 5x5 portfolios on average local connectivity (WCC) and firm-size
This table presents the characteristics of multivariate portfolios. At the beginning of each month, we divide the sample into size quintiles based log market capitalization of previous quarter. Then, we divide each quintile into five groups based on previous month’s weighted clustering coefficiet estimates which proxy for average connectivity. Panel A represents the time-series average of average monthly returns in each portfolio. High-Low is the average difference between High and Low connectivity portfolios. t-stat and p-value corresponds to the t-statistics and p-value of the zero-cost difference portfolio where t-stats are corrected by the Newey-West procedure. Panel B corresponds to the time-series average of the average market capitalization of each portfolio. Panel C corresponds to the time-series averages of the average network density in each portfolio.
Panel A: Average Portfolio Return
Small 2 3 4 Big
Low WCC 0.009 0.001 0.010 0.002 0.000
2 0.001 -0.002 -0.001 0.000 -0.006
3 -0.018 -0.005 -0.014 -0.007 -0.006 4 -0.027 -0.020 -0.006 -0.007 -0.005 High WCC -0.021 -0.009 -0.009 -0.004 -0.004 High-Low -0.030 -0.011 -0.019 -0.006 -0.003 t-stat (-4.39) (-1.68) (-3.56) (-1.19) (-0.61) p-value 0.00 0.05 0.00 0.12 0.27
Panel B: Average Size
Small 2 3 4 Big
Low WCC 1.228 2.437 3.417 4.544 6.218
2 1.995 3.030 3.775 4.677 6.230
3 2.338 3.308 4.032 4.890 6.411
4 2.812 3.845 4.655 5.505 6.948
High WCC 4.245 5.500 6.339 7.414 9.018
Panel C: Average Local Connectivity (WCC)
Small 2 3 4 Big
Low WCC 0.308 0.350 0.360 0.361 0.353
2 0.479 0.485 0.486 0.485 0.484
3 0.559 0.561 0.562 0.563 0.564
4 0.635 0.637 0.640 0.645 0.646
High WCC 0.728 0.746 0.757 0.770 0.821
Table 8: Multivariate Portfolio Analysis : 5x5 portfolios on network reciprocity (RCP) and firm-size
This table presents the characteristics of multivariate portfolios. At the beginning of each month, we divide the sample into size quintiles based log market capitalization of previous quarter.
Then, we divide each quintile into five groups based on previous month’s network reciprocity estimates which proxy for average connectivity. Panel A represents the time-series average of average monthly returns in each portfolio. High-Low is the average difference between High and Low reciprocity portfolios. t-stat and p-value corresponds to the t-statistics and p-value of the zero-cost difference portfolio where t-stats are corrected by the Newey-West procedure. Panel B corresponds to the time-series average of the average market capitalization of each portfolio. Panel C corresponds to the time-series averages of the average reciprocity in each portfolio.
Panel A: Average Portfolio Return
Small 2 3 4 Big
Low RCP 0.005 0.004 -0.002 -0.001 -0.001
2 0.004 0.000 0.001 0.000 -0.001
3 -0.001 -0.002 -0.004 -0.005 -0.010 4 -0.016 -0.010 -0.015 -0.003 -0.003 High RCP -0.030 -0.016 -0.022 -0.018 -0.003 High-Low -0.035 -0.020 -0.020 -0.016 -0.002 t-stat (-5.10) (-3.17) (-3.26) (-3.07) (-0.42) p-value 0.00 0.00 0.00 0.00 0.34
Panel B: Average Size
Small 2 3 4 Big
Low RCP 1.563 3.178 4.398 5.456 6.722
2 2.039 3.329 4.280 5.368 6.938
3 2.252 3.402 4.296 5.393 7.122
4 2.369 3.472 4.375 5.474 7.418
High RCP 2.740 3.967 4.913 6.041 8.342
Panel C: Average Reciprocity (RCP)
Small 2 3 4 Big
Low RCP 0.502 0.546 0.554 0.544 0.551
2 0.651 0.651 0.651 0.650 0.651
3 0.702 0.702 0.703 0.702 0.703
4 0.748 0.749 0.749 0.749 0.750
High RCP 0.806 0.811 0.814 0.814 0.823
Table 9: Multivariate Portfolio Analysis: 5x5 portfolios on global connectivity (network density) and BETA. This table presents the characteristics of multivariate portfolios. At the beginning of each month, we divide sample into beta quintiles based on previous month estimate. Then, we divide each quintile into five groups based on previous month’s network density measures which proxy for global connectivity. Panel A represents the time-series average of average monthly returns in each portfolio. High-Low is the average difference between High and Low connectivity portfolios. t-stat and p-value corresponds to the t-statistics and p-value of the zero-cost difference portfolio where t-stats are corrected by the Newey-West procedure. Panel B corresponds to the time-series average of the average market risk (BETA) of each portfolio. Panel C corresponds to the time-series averages of the average network density in each portfolio.
Panel A: Average Portfolio Return
Low BETA 2 3 4 High BETA
Low ND 0.002 -0.001 0.005 0.003 0.006
2 -0.005 -0.006 -0.003 0.006 0.002
3 -0.020 -0.008 -0.006 -0.005 -0.007
4 -0.018 -0.011 -0.007 -0.008 -0.011
High ND -0.016 -0.013 -0.007 -0.005 -0.018 High-Low -0.018 -0.012 -0.012 -0.007 -0.024 t-stat (-2.57) (-2.49) (-2.27) (-1.37) (-4.11) p-value 0.01 0.01 0.02 0.09 0.00
Panel B: Average BETA
Low BETA 2 3 4 High BETA
Low ND 0.197 0.462 0.590 0.717 0.986
2 0.301 0.561 0.686 0.807 1.049
3 0.292 0.606 0.747 0.882 1.144
4 0.301 0.650 0.798 0.941 1.235
High ND 0.348 0.744 0.918 1.095 1.417
Panel C: Average Network Density (ND)
Low BETA 2 3 4 High BETA
Low ND 0.078 0.078 0.087 0.091 0.092
2 0.138 0.137 0.136 0.133 0.134
3 0.175 0.177 0.179 0.176 0.170
4 0.238 0.240 0.231 0.237 0.232
High ND 0.391 0.318 0.320 0.370 0.331
Table 10: Multivariate Portfolio Analysis: 5x5 portfolios on average local connectivity (WCC) and BETA. This table presents the characteristics of multivariate portfolios. At the beginning of each month, we divide sample into beta quintiles based on previous month estimate. Then, we divide each quintile into five groups based on previous month’s weighted clustering coefficient estimates which proxy for average connectivity. Panel A represents the time-series average of average monthly returns in each portfolio. High-Low is the average difference between High and Low connectivity portfolios. t-stat and p-value corresponds to the t-statistics and p-value of the zero-cost difference portfolio where t-stats are corrected by the Newey-West procedure. Panel B corresponds to the time-series average of the average market risk (BETA) of each portfolio. Panel C corresponds to the time-series averages of the average network density in each portfolio.
Panel A: Average Portfolio Return
Low BETA 2 3 4 High BETA
Low WCC 0.005 0.001 0.004 0.004 0.007
2 -0.006 -0.005 -0.001 0.001 0.005
3 -0.022 -0.012 -0.005 -0.002 -0.011
4 -0.021 -0.013 -0.009 -0.007 -0.016
High WCC -0.010 -0.011 -0.006 -0.006 -0.015 High-Low -0.015 -0.012 -0.010 -0.010 -0.022 t-stat (-2.38) (-2.39) (-1.94) (-1.76) (-3.78) p-value 0.01 0.01 0.03 0.04 0.00
Panel B: Average BETA
Low BETA 2 3 4 High BETA
Low WCC 0.209 0.469 0.598 0.725 0.991
2 0.303 0.563 0.688 0.811 1.047
3 0.282 0.596 0.742 0.881 1.147
4 0.259 0.634 0.792 0.940 1.252
High WCC 0.382 0.751 0.918 1.089 1.403
Panel C: Average Local Connectivity (WCC)
Low BETA 2 3 4 High BETA
Low WCC 0.318 0.343 0.350 0.362 0.358
2 0.482 0.482 0.484 0.483 0.487
3 0.560 0.560 0.561 0.563 0.564
4 0.639 0.639 0.639 0.643 0.643
High WCC 0.747 0.750 0.759 0.772 0.792
Table 11: Multivariate Portfolio Analysis: 5x5 portfolios on network reciprocity (RCP) and BETA.
This table presents the characteristics of multivariate portfolios. At the beginning of each month, we divide sample into beta quintiles based on previous month estimates. Then, we divide each quintile into five groups based on previous month’s network reciprocity estimates. Panel A rep-resents the time-series average of average monthly returns in each portfolio. High-Low is the average difference between High and Low reciprocity portfolios. t-stat and p-value corresponds to the t-statistics and p-value of the zero cost difference portfolio where t-stats are corrected by the Newey-West procedure. Panel B corresponds to the time-series average of the average market risk (BETA) of each portfolio. Panel C corresponds to the time-series averages of the average reciprocity in each portfolio.
Panel A: Average Portfolio Return
Low BETA 2 3 4 High BETA
Low RCP 0.003 -0.002 0.000 0.005 0.000
2 0.001 -0.003 -0.002 0.004 0.002
3 -0.008 -0.006 -0.001 -0.003 -0.003
4 -0.018 -0.014 -0.010 -0.001 -0.006
High RCP -0.029 -0.013 -0.012 -0.015 -0.020 High-Low -0.032 -0.011 -0.012 -0.020 -0.020 t-stat (-4.82) (-2.00) (-2.12) (-3.82) (-3.34) p-value 0.00 0.02 0.02 0.00 0.00
Panel B: Average BETA
Low BETA 2 3 4 High BETA
Low RCP 0.218 0.472 0.601 0.734 0.998
2 0.326 0.574 0.702 0.827 1.060
3 0.341 0.618 0.750 0.882 1.134
4 0.326 0.649 0.797 0.942 1.221
High RCP 0.215 0.678 0.880 1.079 1.447
Panel C: Average Network Reciprocity (RCP)
Low BETA 2 3 4 High BETA
Low RCP 0.510 0.535 0.545 0.557 0.551
2 0.650 0.649 0.650 0.651 0.653
3 0.702 0.702 0.702 0.703 0.704
4 0.748 0.748 0.749 0.749 0.750
High RCP 0.813 0.808 0.808 0.812 0.826
Table 12: Fama-French four-factor Results - We run the following regression on the time series of monthly returns of five zero-cost connectivity-size portfolios: Rp=#1p+#2pRm+#3pSM B+#4pHM L+#5pU M D+✏p. The sample period is between January 2006 -November 2015. Panel A provides the results for multivariate portfolios constructed using the global connectivity measure (network density). Panel B provides the results for multivariate portfolios constructed using the average local connectivity measure (weighted clustering coefficient). Panel C provides the results for multivariate portfolios constructed using the network reciprocity. We provide the coefficient estimates and their respective t-statistics in the table. For goodness of fit, we provide adjustedR2 measures along with F statistics. Last two rows, provide theGibbons et al.(1989) test statistics for the null hypothesis that ˆ#1= 0.
Panel A: Global Connectivity (ND) - Size Portfolios
Small 2 3 4 Big
Panel B: Local Connectivity (WCC) - Size Portfolios
Small 2 3 4 Big
Table 13: Fama-MacBeth Regressions for global connectivity (network density):
This table presents the results of Fama-MacBeth regressions. Ri,t+h= 0,t+ 1,tN Di,t+ 2,tBET Ai,t+ 3,tSIZEi,t+ 4,tBT Mi,t+
5,t0 Xi,t+✏i,tEach month, we regress the stock returns on previous months network density measure (N D) along with the control factors BETA, SIZE, BTM, MOM, REV, ILLIQ, MAX and IVOL. Entries in the table are the time-series averages of the slope coefficients obtained from the cross-sectional regressions. Values in parenthesis present the corresponding t-statistics calculated usingNewey and West(1987) standard errors. Panel A,B and C present the results for a holding period (h) of 1-month, 3 months and 6 months, respectively. ***,**,* indicates statistical significance at 1%, 5%, 10%, respectively.
Panel A: Holding Period = 1 month
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
ND -0.044 -0.051 -0.063 -0.041 -0.044 -0.039 -0.033 -0.033 -0.048 -0.043
(3.330)*** (4.243)*** (4.712)*** (3.074)*** (3.309)*** (3.067)*** (2.337)** (2.302)** (3.647)*** (3.145)***
BETA 0.008 0.002
Intercept 0.003 -0.002 -0.003 0.003 0.001 0.001 0.012 0.016 0.002 0.007
(0.291) (0.275) (0.278) (0.321) (0.119) (0.143) (1.150) (1.578) (0.222) (0.671)
R2 0.01 0.02 0.03 0.03 0.04 0.02 0.03 0.04 0.04 0.11
N 37,328 37,326 37,328 37,328 36,778 37,324 37,328 37,326 37,328 36,772
Panel B: Holding Period = 3 months
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
ND -0.029 -0.034 -0.042 -0.027 -0.029 -0.029 -0.021 -0.023 -0.030 -0.038
(2.165)** (2.552)** (3.014)*** (1.964)* (2.191)** (2.183)** (1.467) (1.590) (2.168)** (2.823)***
BETA 0.005 0.001
Intercept -0.001 -0.003 -0.005 -0.001 -0.002 -0.001 0.004 0.006 -0.001 -0.003
(0.079) (0.347) (0.506) (0.077) (0.240) (0.092) (0.422) (0.636) (0.096) (0.295)
R2 0.01 0.02 0.03 0.03 0.03 0.02 0.03 0.03 0.02 0.09
N 36,464 36,463 36,464 36,464 35,925 36,460 36,464 36,463 36,464 35,920
Panel C: Holding Period = 6 months
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
ND -0.018 -0.021 -0.029 -0.016 -0.020 -0.016 -0.014 -0.015 -0.020 -0.026
(1.323) (1.549) (2.133)** (1.166) (1.467) (1.150) (0.989) (1.024) (1.505) (1.773)*
BETA 0.004 -0.000
Intercept 0.001 -0.001 -0.003 0.001 -0.001 0.000 0.003 0.005 0.001 -0.002
(0.092) (0.113) (0.286) (0.156) (0.113) (0.035) (0.336) (0.527) (0.057) (0.152)
2
Table 14: Fama-MacBeth Regressions for average local network connectivity (WCC):
This table presents the results of Fama-MacBeth regressions. Ri,t+h= 0,t+ 1,tW CCi,t+ 2,tBET Ai,t+ 3,tSIZEi,t+ 4,tBT Mi,t+
5,t0 Xi,t+✏i,t. Each month, we regress the stock returns on previous months average local connectivity measure (W CC) along with the control factors BETA, SIZE, BTM, MOM, REV, ILLIQ, MAX, and IVOL. Entries in the table are the time-series averages of the slope coefficients obtained from the cross-sectional regressions. Values in parenthesis present the corresponding t-statistics calculated usingNewey and West(1987) standard errors. Panel A,B and C present the results for a holding period (h) of 1-month, 3 months and 6 months, respectively. ***,**,* indicates statistical significance at 1%, 5%, 10%, respectively.
Panel A: Holding Period = 1 month
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
WCC -0.036 -0.042 -0.051 -0.034 -0.036 -0.034 -0.029 -0.030 -0.040 -0.037
(3.753)*** (4.640)*** (5.162)*** (3.452)*** (3.751)*** (3.584)*** (2.867)*** (2.874)*** (4.084)*** (3.804)***
BETA 0.008 0.002
Intercept 0.015 0.011 0.013 0.014 0.013 0.014 0.022 0.027 0.015 0.019
(1.576) (1.284) (1.293) (1.512) (1.391) (1.396) (2.239)** (2.697)*** (1.662)* (2.064)**
R2 0.01 0.02 0.03 0.03 0.04 0.02 0.03 0.04 0.04 0.11
N 37,328 37,326 37,328 37,328 36,778 37,324 37,328 37,326 37,328 36,772
Panel B: Holding Period = 3 months
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
WCC -0.022 -0.026 -0.033 -0.020 -0.022 -0.022 -0.017 -0.019 -0.023 -0.029
(2.224)** (2.642)*** (3.066)*** (1.981)* (2.194)** (2.190)** (1.629) (1.785)* (2.261)** (2.771)***
BETA 0.005 0.001
Intercept 0.006 0.005 0.004 0.006 0.004 0.006 0.010 0.012 0.006 0.006
(0.726) (0.564) (0.485) (0.639) (0.516) (0.700) (1.121) (1.412) (0.749) (0.630)
R2 0.02 0.02 0.03 0.03 0.03 0.02 0.03 0.03 0.03 0.09
N 36,464 36,463 36,464 36,464 35,925 36,460 36,464 36,463 36,464 35,920
Panel C: Holding Period = 6 months
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
WCC -0.011 -0.012 -0.019 -0.010 -0.012 -0.009 -0.008 -0.009 -0.013 -0.015
(1.082) (1.202) (1.804)* (0.916) (1.194) (0.823) (0.786) (0.853) (1.253) (1.264)
BETA 0.003 -0.001
Intercept 0.004 0.003 0.002 0.004 0.002 0.002 0.006 0.008 0.004 0.004
(0.429) (0.301) (0.276) (0.433) (0.250) (0.262) (0.637) (0.870) (0.445) (0.381)
2
Table 15: Fama-MacBeth Regressions for network reciprocity:
This table presents the results of Fama-MacBeth regressions.Ri,t+h= 0,t+ 1,tRCPi,t+ 2,tBET Ai,t+ 3,tSIZEi,t+ 4,tBT Mi,t+
5,t0 Xi,t+✏i,t. Each month, we regress the stock returns on previous months network reciprocity measures (RCP) along with the control factors BETA, SIZE, BTM, MOM, REV, ILLIQ, MAX, and IVOL. Entries in the table are the time-series averages of the slope coefficients obtained from the cross-sectional regressions. Values in parenthesis present the corresponding t-statistics calculated using Newey and West(1987) standard errors. Panel A,B and C present the results for a holding period (h) of 1-month, 3 months and 6 months, respectively. ***,**,* indicates statistical significance at 1%, 5%, 10%, respectively.
Panel A: Holding Period = 1 month
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
RCP -0.069 -0.075 -0.070 -0.064 -0.068 -0.066 -0.052 -0.048 -0.073 -0.037
(5.073)*** (5.804)*** (5.207)*** (4.752)*** (4.983)*** (4.700)*** (3.508)*** (3.150)*** (5.295)*** (2.590)**
BETA 0.006 -0.001
Intercept 0.043 0.042 0.040 0.040 0.040 0.040 0.041 0.042 0.043 0.032
(3.948)*** (3.972)*** (3.560)*** (3.773)*** (3.805)*** (3.422)*** (3.987)*** (4.194)*** (4.128)*** (3.054)***
R2 0.02 0.03 0.03 0.02 0.04 0.02 0.03 0.04 0.04 0.11
N 37,328 37,326 37,328 37,328 36,778 37,324 37,328 37,326 37,328 36,772
Panel B: Holding Period = 3 months
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
RCP -0.048 -0.052 -0.050 -0.043 -0.048 -0.048 -0.038 -0.038 -0.049 -0.039
(3.438)*** (3.819)*** (3.614)*** (3.049)*** (3.474)*** (3.381)*** (2.606)** (2.604)** (3.425)*** (2.893)***
BETA 0.005 0.000
Intercept 0.027 0.027 0.026 0.024 0.026 0.028 0.026 0.027 0.027 0.021
(3.067)*** (3.010)*** (2.769)*** (2.746)*** (2.907)*** (2.805)*** (3.032)*** (3.193)*** (3.115)*** (2.283)**
R2 0.01 0.02 0.03 0.02 0.03 0.02 0.02 0.03 0.02 0.09
N 36,464 36,463 36,464 36,464 35,925 36,460 36,464 36,463 36,464 35,920
Panel C: Holding Period = 6 months
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
RCP -0.029 -0.030 -0.032 -0.026 -0.027 -0.026 -0.024 -0.023 -0.031 -0.019
(2.181)** (2.342)** (2.442)** (1.863)* (2.051)** (1.902)* (1.762)* (1.643) (2.353)** (1.387)
BETA 0.003 -0.000
Intercept 0.018 0.016 0.017 0.016 0.015 0.016 0.017 0.018 0.019 0.010
(2.150)** (1.948)* (1.983)** (1.955)* (1.784)* (1.704)* (2.077)** (2.174)** (2.240)** (1.068) 2
Table 16: Transition Matrix: In this table, we present the transition probabilities. Panel A, B and
Table 16: Transition Matrix: In this table, we present the transition probabilities. Panel A, B and